This paper presents an initial value solution for a discrete form of the Fr
edholm integral equation of the second kind whose Fredholm resolvent kernel
satisfies in digital communication and estimation theory. The solution is
called the Sugisaka-Ueno Chandrasekhar algorithm based on Ueno and Chandras
ekhar's original works on invariant imbedding in radiative transfer can be
calculated in on-line fashion. The filtering formula obtained from this res
earch is completely different from the Wiener and Kalman formulas. A simula
tion study is shown. (C) 2000 Elsevier Science Inc. All rights reserved.